The fishing industry is a relatively small part of the national economy. Just 0.1% of employed people in the United States are employed in fishing, hunting and trapping combined (about 10,000 people). Perhaps another 2,000-5,000 people (about 1-2 per fishing business) are self-employed fishermen (or fisherwomen). There are places, however, like Alaska and Maine where fishing is an important part of the economy.
The dominant issue in the fishing industry is declining fishing stocks. Simply put, most fishing is not agriculture (although "fish farms" are beginning to provide a larger part of the total supply). Fishing is a form of hunting that takes place in oceans, seas, lakes and rivers. Imagine hunters trying to feed the population of the United States by hunting deer, rabbits and ducks and the nature of the problem becomes clear.
As demand for fish has risen with growth in the United States and world populations, the intensity of fishing has increased. This has been aided by technological innovations that have made it easier for fishermen to catch fish. More intense and more effective fishing has resulted in a greater share of the fisheries being fished each season. This, in turn, has led to ever declining fish populations, which because they are smaller also reproduce at lower rates.
The effect has been most pronounced amongst top of the foodchain predator fish which are often most prized for food purposes. Sharks, tuna, salomn and swordfish, for example, are all predators of the sea. Ecologically, they are in the same position as the lions and hyenas of the Savannah, or the wolves, mountain lions and lynx of the American West.
The problem of hunters overhunting and depleting the wild animal resource is a version of an economic problem called the "tragedy of the commons" which is a classic failure of a free market laissez faire approach to the economy. Individually, the incentive for each fisherman is to fish as much as possible each season. But, for fishermen as a whole, this depletes the resource and reduces aggregate returns. For hunters on land, this is usually resolved with a system of state regulation that imposes limits on how much each hunter can hunt each year, and with limits on the technologies that can be used to hunt (e.g. most states have fairly long bow hunting seasons, and fairly short rifle hunting seasons).
At sea, there has been no one government to regulate fishing, although international treaties have greatly reducing "whaling" (the fishing of whales). The Law of the Sea Treaty seeks to remedy this failure so that fishing can be controlled to sustainable levels.
The other big problem in the fishing industry has been pollution with heavy metals, particularly mercury. Small levels of heavy metals enter the bodies of fish and plants at the bottom of the food pyramid and stay there. At each successive level of the food pyramid (fish that eat plants, fish that eat fish that eat plants, fish that eat first level predator fish), heavy metal concretrations increase. And, since high level predators in the ocean ecosystem are the most popular fish to eat, this impacts the safety of those fish for human consumption.